Mean Absolute Deviation Worksheets - Free Printable

Let’s solve each problem step by step. We’ll find the mean absolute deviation (MAD) for each data set.

What is Mean Absolute Deviation?

It tells us how far, on average, each number in a data set is from the mean (average). Here’s how to calculate it:

1. Find the mean of the data set.
2. For each number, find the difference between that number and the mean.
3. Take the absolute value of each difference (make it positive).
4. Add up all those absolute values → that’s the “Sum”.
5. Divide the sum by the number of data points → that’s the MAD.

We’ll round answers to two decimal places.

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## Problem 1: Data Set = 12, 19, 10, 18, 21

Step 1: Find the mean
Add them: 12 + 19 + 10 + 18 + 21 = 80
Divide by 5 numbers: 80 ÷ 5 = 16

Step 2: Find differences from mean (each number minus 16)
- 12 - 16 = -4
- 19 - 16 = 3
- 10 - 16 = -6
- 18 - 16 = 2
- 21 - 16 = 5

Step 3: Absolute values
| -4 | = 4
| 3 | = 3
| -6 | = 6
| 2 | = 2
| 5 | = 5

Step 4: Sum of absolute values
4 + 3 + 6 + 2 + 5 = 20

Step 5: Divide by number of data points (5)
20 ÷ 5 = 4.00

✔ Mean Absolute Deviation = 4.00

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## Problem 2: Data Set = 7, 14, 11, 13, 4, 20

Step 1: Find the mean
Add them: 7 + 14 + 11 + 13 + 4 + 20 = 69
Divide by 6 numbers: 69 ÷ 6 = 11.5

Step 2: Differences from mean (each number minus 11.5)
- 7 - 11.5 = -4.5
- 14 - 11.5 = 2.5
- 11 - 11.5 = -0.5
- 13 - 11.5 = 1.5
- 4 - 11.5 = -7.5
- 20 - 11.5 = 8.5

Step 3: Absolute values
| -4.5 | = 4.5
| 2.5 | = 2.5
| -0.5 | = 0.5
| 1.5 | = 1.5
| -7.5 | = 7.5
| 8.5 | = 8.5

Step 4: Sum of absolute values
4.5 + 2.5 + 0.5 + 1.5 + 7.5 + 8.5 = let’s add step by step:
4.5 + 2.5 = 7
7 + 0.5 = 7.5
7.5 + 1.5 = 9
9 + 7.5 = 16.5
16.5 + 8.5 = 25

Step 5: Divide by 6
25 ÷ 6 ≈ 4.166... → rounded to two decimals = 4.17

✔ Mean Absolute Deviation = 4.17

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## Problem 3: Data Set = 50, 48, 36, 45, 33, 37

Step 1: Find the mean
Add them: 50 + 48 + 36 + 45 + 33 + 37 =
50+48=98; 98+36=134; 134+45=179; 179+33=212; 212+37=249
Divide by 6: 249 ÷ 6 = 41.5

Step 2: Differences from mean (each number minus 41.5)
- 50 - 41.5 = 8.5
- 48 - 41.5 = 6.5
- 36 - 41.5 = -5.5
- 45 - 41.5 = 3.5
- 33 - 41.5 = -8.5
- 37 - 41.5 = -4.5

Step 3: Absolute values
|8.5| = 8.5
|6.5| = 6.5
|-5.5| = 5.5
|3.5| = 3.5
|-8.5| = 8.5
|-4.5| = 4.5

Step 4: Sum of absolute values
8.5 + 6.5 = 15
15 + 5.5 = 20.5
20.5 + 3.5 = 24
24 + 8.5 = 32.5
32.5 + 4.5 = 37

Step 5: Divide by 6
37 ÷ 6 ≈ 6.166... → rounded to two decimals = 6.17

✔ Mean Absolute Deviation = 6.17

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## Problem 4: Data Set = 8, 5, 2, 9

Step 1: Find the mean
Add them: 8 + 5 + 2 + 9 = 24
Divide by 4: 24 ÷ 4 = 6

Step 2: Differences from mean (each number minus 6)
- 8 - 6 = 2
- 5 - 6 = -1
- 2 - 6 = -4
- 9 - 6 = 3

Step 3: Absolute values
|2| = 2
|-1| = 1
|-4| = 4
|3| = 3

Step 4: Sum of absolute values
2 + 1 + 4 + 3 = 10

Step 5: Divide by 4
10 ÷ 4 = 2.50

✔ Mean Absolute Deviation = 2.50

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Final Answer:
1) 4.00
2) 4.17
3) 6.17
4) 2.50